Finite Group Databasebeta

← #29697662

Subgroups — #29697662

Order 15616.

822 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D61C211yesmaximal, characteristic
2#21448695C211yesmaximal, characteristic
3#21448692C211yesmaximal, characteristic
4#21446551C211yesmaximal, characteristic, complemented
5#21446549C211yesmaximal, characteristic, complemented
6#21446413C211yesmaximal, characteristic, complemented
7#21446412C211yesmaximal, characteristic, complemented
8#21446410C211yesmaximal, characteristic, complemented
9#21445908C211yesmaximal, characteristic
10#21445908C211yesmaximal, characteristic
11#21445847C211yesmaximal, characteristic
12C4×#14519710C211yesmaximal, characteristic, complemented
13#21445711C211yesmaximal, characteristic, complemented
14#21445589C211yesmaximal, characteristic
15C61×#1921C211yesmaximal, characteristic, complemented
16C22×C8×D61C2211yescharacteristic
17C2×C4⋊C4×D61C2211yescharacteristic
18C2×C4⋊C4×D61C2211yescharacteristic
19C2×#14519711C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24#107×D61C418yescomplemented
25C2×#14519689C2211yescharacteristic
26C2×C4×#92418C2211yescharacteristic
27C2×C8×Dic61C2211yescharacteristic
28#16839661C2211yescharacteristic
29#16839660C2211yescharacteristic
30#16839658C2211yescharacteristic
31#16839649—21no—
32#16839646—21no—
33#16839644—21no—
34#16839643—21no—
35#16839621—21no—
36#16839619—21no—
37#16839619C2211yescharacteristic
38#16839619C2211yescharacteristic
39C4⋊C4×Dic61C2211yescharacteristic
40C4⋊C4×Dic61C2211yescharacteristic
41C4×C4⋊Dic61C2211yescharacteristic
42C4×#11758198—21no—
43C4×#11758198C2211yescharacteristic
44#16839609—21no—
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53C2×#107×C61C2211yescharacteristic
54C61×#389C2211yescharacteristic
55C4×C4⋊C4×C61C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C22×C4×D61—21no—
61C22×C4×D61—21no—
62C22×C4×D61C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C2×C8×D61—22no—
66C2×C8×D61—22no—
67C2×C8×D61C2×C414yes—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C4⋊C4×D61—22no—
78C4⋊C4×D61—22no—
79C4⋊C4×D61C2×C414yes—
80C4⋊C4×D61C2×C414yes—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198D411yescharacteristic
84C2×#11758198D411yescharacteristic
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61C2311yescharacteristic
89#14519711C2×C414yes—
90#14519710—22no—
91#14519710—22no—
92#14519710C2×C414yes—
93#14519710C2×C414yes—
94#14519689—22no—
95C4×#92418—22no—
96C8×Dic61—22no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684D411yescharacteristic
106#14519684D411yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C42×C61—21no—
115C2×C42×C61C2311yescharacteristic
116#107×C61C2×C414yes—
117#95×C61—21no—
118#95×C61—21no—
119C23×D61C2×D411yescharacteristic
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2411yescharacteristic
127C22×Dic61—21no—
128C22×Dic61—21no—
129C22×Dic61—21no—
130C22×Dic61—21no—
131C22×Dic61C2×D411yescharacteristic
132C22×Dic61C2×D411yescharacteristic
133C22×Dic61C2×D411yescharacteristic
134C2×C4×D61—21no—
135C2×C4×D61—21no—
136C2×C4×D61—21no—
137C2×C4×D61—21no—
138C2×C4×D61—24no—
139C2×C4×D61—24no—
140C2×C4×D61—81no—
141C2×C4×D61—81no—
142C2×C4×D61—81no—
143C2×C4×D61—81no—
144C2×C4×D61C22×C412yes—
145C2×C4×D61#4112yes—
146C2×C8×C61—21no—
147C2×C8×C61—21no—
148C2×C8×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61C22×C412yes—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—81no—
159C4⋊C4×C61C22×C412yes—
160C4⋊C4×C61C22×C412yes—
161C42×C61—21no—
162C42×C61—21no—
163C42×C61—81no—
164#11758198—22no—
165#11758198—42no—
166#11758198—42no—
167#11758198Q1614yes—
168C4⋊Dic61—21no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—81no—
175C4⋊Dic61C22×C412yes—
176C4⋊Dic61C22×C412yes—
177#11758196—24no—
178#11758196—24no—
179#11758196—81no—
180#11758196—81no—
181C4×Dic61—21no—
182C4×Dic61—21no—
183C4×Dic61—81no—
184C4×Dic61—81no—
185C4×Dic61—81no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418C22×C412yes—
190C2×#92418#4112yes—
191C2×#92418#4112yes—
192C8×D61—28no—
193C23×C61C22×D411yescharacteristic
194C22×D61—21no—
195C22×D61—21no—
196C22×D61—21no—
197C22×D61—21no—
198C22×D61C4×D412yes—
199C22×D61C2×Q1612yes—
200C22×D61#13512yes—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—22no—
204C2×C4×C61—22no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—41no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61C2×Q1612yes—
219C2×C4×C61C23×C411yescharacteristic
220C2×C4×C61C2×#4111yescharacteristic
221C2×C4×C61C2×#4111yescharacteristic
222C2×C4×C61C2×#4111yescharacteristic
223C2×C4×C612−1+411yescharacteristic
224C2×C4×C612−1+411yescharacteristic
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—22no—
230C2×Dic61—22no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61C4×D412yes—
245C2×Dic61C2×Q1612yes—
246C4×D61—22no—
247C4×D61—22no—
248C4×D61—22no—
249C4×D61—22no—
250C4×D61—84no—
251C4×D61—84no—
252C8×C61—22no—
253C8×C61—41no—
254#92418—41no—
255#92418#11714yes—
256#22612—611nomaximal, Sylow
257C22×C61C2×C4×D411yescharacteristic
258C22×C61#54711yescharacteristic
259C22×C61#54711yescharacteristic
260C22×C61C22×Q1611yescharacteristic
261C22×C61C2×#13511yescharacteristic
262C22×C61#57611yescharacteristic
263C22×C61#57611yescharacteristic
264C2×D61—22no—
265C2×D61—22no—
266C2×D61—22no—
267C2×D61—22no—
268C2×D61—22no—
269C2×D61—22no—
270C2×D61C4×Q1614yes—
271C4×C61—22no—
272C4×C61—41no—
273C4×C61—42no—
274C4×C61—42no—
275C4×C61—81no—
276C4×C61—81no—
277C4×C61C2×#11711yescharacteristic
278C4×C61#51911yescharacteristic
279C4×C61#55211yescharacteristic
280C4×C61#55211yescharacteristic
281Dic61—22no—
282Dic61—22no—
283Dic61—41no—
284Dic61—42no—
285Dic61—42no—
286Dic61—81no—
287Dic61—81no—
288C22×#107—611no—
289#2345—611no—
290#2345—611no—
291#1942—611no—
292#1942—611no—
293#1921—611no—
294#1921—611no—
295#1921—611no—
296#1921D6111yescharacteristic, complemented
297#1824—611no—
298#1824—611no—
299#1808—611no—
300C4×#107—611no—
301C4×#107—611no—
302C8×C22⋊C4—611no—
303C2×C61#234411yescharacteristic
304C2×C61C2×C4×Q1611yescharacteristic
305C2×C61#294811yescharacteristic
306C2×C61#333811yescharacteristic
307C2×C61#333811yescharacteristic
308C2×C61#333911yescharacteristic
309C2×C61#333911yescharacteristic
310D61—24no—
311C23×C8—611no—
312C22×C4⋊C4—611no—
313C22×C4⋊C4—611no—
314C2×#107—611no—
315C2×#107—611no—
316C2×#107—611no—
317C2×#107—618no—
318C2×#107—611no—
319C2×#107—611no—
320C2×#107C2×D6111yescharacteristic
321C2×C22⋊C8—611no—
322C2×C4×C8—611no—
323C2×C4×C8—611no—
324#389—611no—
325#389—611no—
326#389—611no—
327#389C2×D6111yescharacteristic
328#387—1221no—
329#387—1221no—
330#387—1221no—
331#387—1221no—
332#380—611no—
333#380—611no—
334#380—1221no—
335#380—1221no—
336C4×C4⋊C4—611no—
337C4×C4⋊C4—611no—
338C4×C4⋊C4—611no—
339C4×C4⋊C4C2×D6111yescharacteristic
340C4×C22⋊C4—611no—
341C4×C22⋊C4—1221no—
342C4×C22⋊C4—1221no—
343#340—611no—
344#340—611no—
345#340—611no—
346#340—611no—
347#340—611no—
348#340—611no—
349#340—611no—
350#340C2×D6111yescharacteristic
351#340C2×D6111yescharacteristic
352#340C2×D6111yescharacteristic
353#336—611no—
354#336C2×D6111yescharacteristic
355C61#2261211yescharacteristic, complemented, Sylow
356C23×C4—611no—
357C23×C4—1221no—
358C23×C4—1221no—
359C22×C8—611no—
360C22×C8—614no—
361C22×C8—611no—
362C22×C8—1222no—
363C22×C8—1222no—
364C22×C8C22×D6111yescharacteristic
365C22×C8C22×D6111yescharacteristic
366C2×C4⋊C4—21no—
367C2×C4⋊C4—611no—
368C2×C4⋊C4—611no—
369C2×C4⋊C4—614no—
370C2×C4⋊C4—614no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—1222no—
374C2×C4⋊C4—1222no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4—1221no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4C22×D6111yescharacteristic
381C2×C4⋊C4C22×D6111yescharacteristic
382C2×C4⋊C4C22×D6111yescharacteristic
383C2×C4⋊C4C22×D6111yescharacteristic
384C2×C22⋊C4—611no—
385C2×C22⋊C4—611no—
386C2×C22⋊C4—1221no—
387C2×C22⋊C4—1221no—
388C2×C42—21no—
389C2×C42—611no—
390C2×C42—1221no—
391C2×C42—1221no—
392C2×C42—1221no—
393C2×C42C22×D6111yescharacteristic
394#107—614no—
395#107—614no—
396#107—614no—
397#107—1222no—
398#107—1222no—
399#107C4×D6114yes—
400C22⋊C8—1222no—
401C4×C8—1222no—
402C4×C8—1222no—
403#95—21no—
404#95—21no—
405#95—611no—
406#95—611no—
407#95—1221no—
408#95—1221no—
409#95—1221no—
410#95—1221no—
411#95—1221no—
412#95—1221no—
413#95—1221no—
414#95—1221no—
415C24—611no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—611no—
421C22×C4—611no—
422C22×C4—612no—
423C22×C4—612no—
424C22×C4—611no—
425C22×C4—1224no—
426C22×C4—1224no—
427C22×C4—1221no—
428C22×C4—1221no—
429C22×C4—1221no—
430C22×C4—1221no—
431C22×C4—1221no—
432C22×C4—1221no—
433C22×C4—1221no—
434C22×C4—1221no—
435C22×C4—4881no—
436C22×C4—4881no—
437C22×C4—4881no—
438C22×C4—4881no—
439C22×C4D4×D6111yescharacteristic
440C22×C4D4×D6111yescharacteristic
441C22×C4C23×D6111yescharacteristic
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—612no—
448C2×C8—612no—
449C2×C8—612no—
450C2×C8—1228no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8C2×C4×D6112yes—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—81no—
462C4⋊C4—612no—
463C4⋊C4—612no—
464C4⋊C4—1224no—
465C4⋊C4—1224no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—4881no—
473C4⋊C4—4881no—
474C4⋊C4—4881no—
475C4⋊C4C2×C4×D6112yes—
476C4⋊C4C2×C4×D6112yes—
477C22⋊C4—614no—
478C22⋊C4—1222no—
479C22⋊C4—2442no—
480C22⋊C4—2442no—
481C42—21no—
482C42—21no—
483C42—81no—
484C42—1221no—
485C42—1221no—
486C42—4881no—
487C42—4881no—
488C42—4881no—
489C23—612no—
490C23—612no—
491C23—612no—
492C23—1221no—
493C23—1221no—
494C23—1221no—
495C23—1221no—
496C23C2×D4×D6111yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—612no—
515C2×C4—612no—
516C2×C4—1221no—
517C2×C4—1221no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4—1222no—
521C2×C4—1222no—
522C2×C4—1222no—
523C2×C4—1222no—
524C2×C4—1222no—
525C2×C4—1222no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—4884no—
530C2×C4—4884no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4Q16×D6112yes—
542C2×C4C22×C4×D6111yescharacteristic
543C2×C4#41×D6111yescharacteristic
544C2×C4#41×D6111yescharacteristic
545C2×C4#41×D6111yescharacteristic
546C2×C4#1451982411yescharacteristic
547C2×C4#1451982511yescharacteristic
548C8—22no—
549C8—41no—
550C8—614no—
551C8—2441no—
552C22—614no—
553C22—1222no—
554C22—1222no—
555C22—1222no—
556C22—1222no—
557C22—1222no—
558C22—1222no—
559C22C4×D4×D6111yescharacteristic
560C22#1684041011yescharacteristic
561C22#1684041411yescharacteristic
562C22C2×Q16×D6111yescharacteristic
563C22#135×D6111yescharacteristic
564C22#1684056611yescharacteristic
565C22#1684056611yescharacteristic
566C4—22no—
567C4—41no—
568C4—42no—
569C4—42no—
570C4—81no—
571C4—81no—
572C4—1222no—
573C4—1222no—
574C4—4881no—
575C4—4881no—
576C4—2441no—
577C4—2442no—
578C4—2442no—
579C4#117×D6111yescharacteristic
580C4#1684023811yescharacteristic
581C4#1684044411yescharacteristic
582C4#1684044811yescharacteristic
583C2—1224no—
584C2#2144868511yescharacteristic
585C2C4×Q16×D6111yescharacteristic
586C2#2145466811yescharacteristic
587C2#2145820611yescharacteristic
588C2#2145821011yescharacteristic
589C2#2145821411yescharacteristic
590C2#2145821811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1921C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenter#1921D61
hypocenterC61#22612
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #21446551C2semidirect
5. #21446549C2semidirect
6. #21446413C2semidirect
7. #21446412C2semidirect
8. #21446410C2semidirect
12. C4×#14519710C2semidirect
13. #21445711C2semidirect
15. C61×#1921C2semidirect
24. #107×D61C4semidirect
296. #1921D61semidirect
355. C61#22612semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#107×D612
#214486952
#214486922
#214465512
#214465492
#214464132
#214464122
#214464102
#214459082
#214458472
C4×#145197102
#214457112
#214455892
C61×#19212
#2261261